Semiconductor Device Physicseng.staff.alexu.edu.eg/~mmorsy/Courses/Undergraduate/EE336... ·...

1

Lecture 7

Semiconductor Device Physics

http://zitompul.wordpress.com

2 0 1 3

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Chapter 6pn Junction Diodes: I-V Characteristics


3

Majority

carriers

Majority

carriers

Qualitative Derivation

Chapter 6 pn Junction Diodes: I-V Characteristics

4

Current Flow in a pn Junction Diode


When a forward bias (VA > 0) is applied, the potential barrier to diffusion across the junction is reduced.

Minority carriers are “injected” into the quasi-neutral regions Δnp > 0, Δpn > 0.

Minority carriers diffuse in the quasi-neutral regions, recombining with majority carriers.

5

Ideal Diode: Assumptions


Steady-state conditions.

Non-degenerately doped step junction.

One-dimensional diode.

Low-level injection conditions prevail in the quasi-neutral regions.

No processes other than drift, diffusion, and thermal R–G take place inside the diode.

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N n N n N

( )( )

dn d nx q n qD q n qD

dx dx

J E E

P p P p P

( )( )

dp d px q p qD q p qD

dx dx

J E E

Current Flow in a pn Junction Diode


Current density J = JN(x) + JP(x)

JN(x) and JP(x) may vary with position, but J is constant throughout the diode.

Yet an additional assumption is now made, that thermal recombination-generation is negligible throughout the depletion region JN and JP are therefore determined to be constants independent of position inside the depletion region.

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n-sidep-side

p0 p A

2

ip0 p

A

( )

( )

p x N

nn x

N

n0 n D

2

in0 n

D

( )

( )

n x N

np x

N

p p A( )p x N n n D( )n x N

Carrier Concentrations at –xp, +xn


Consider the equilibrium carrier concentrations at VA = 0:

If low-level injection conditions prevail in the quasi-neutral

regions when VA 0, then:

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i P

N i

( )

i( )

i

E F kT

F E kT

p n e

n n e

A2

i qV kTnp n e

N ii P

N P

( )( )2

i

( )2

i

F E kTE F kT

F F kT

np n e e

n e

p nfor x x x

“Law of the Junction”


The voltage VA applied to a pn junction falls mostly across the depletion region (assuming that low-level injection conditions prevail in the quasi-neutral regions).

Two quasi-Fermi levels is drawn in the depletion region:

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p p A( )p x N

n-sidep-side

n n D( )n x N

A

2

ip p

A

( ) ( 1)qV kTn

n x eN

A

2

in n

D

( ) ( 1)qV kTn

p x eN

Excess Carrier Concentrations at –xp, xn


A

A

2

ip p

A

p0

( )

qV kT

qV kT

n en x

N

n e

A

A

2

in n

D

n0

( )

qV kT

qV kT

n ep x

N

p e

10

A 0.6 0.02586 12 3

p p p0( ) 100 1.192 10 cmqV kTn x n e e

12 12 3

p p p p p0( ) ( ) 1.192 10 100 1.192 10 cmn x n x n

Example: Carrier Injection


A pn junction has NA=1018 cm–3 and ND=1016 cm–3. The applied voltage is 0.6 V.

a) What are the minority carrier concentrations at the depletion-region edges?

b) What are the excess minority carrier concentrations?

A 4 0.6 0.02586 14 3

n n n0( ) 10 1.192 10 cmqV kTp x p e e

14 4 14 3

n n n n n0( ) ( ) 1.192 10 10 1.192 10 cmp x p x p

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A

n n n0( ) ( 1)qV kTp x p e

2

n nP 2

p

0 , 0d p p

D xdx

P P

n 1 2( )x L x L

p x Ae A e

0x 0 x

P P pL D

Excess Carrier Distribution

for 0x


From the minority carrierdiffusion equation,

We have the following boundary conditions:

n ( ) 0p

For simplicity, we develop a new coordinate system:

Then, the solution is given by:

• LP : hole minority carrier diffusion length

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Excess Carrier Distribution

A

n n0( 0) ( 1)qV kT

p x p e

n ( ) 0p x

A P

n n0( ) ( 1) , 0qV kT x L

p x p e e x

P P'/ '/

n 1 2( )x L x L

p x Ae A e

NA

p p0( ) ( 1) , 0x LqV kTn x n e e x

A /

1 n0( 1)qV kTA p e

2 0A


New boundary conditions

From the x’ → ∞,

From the x’ → 0,

Therefore

Similarly,

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A Pn PP P n0

P

( )( ) ( 1)

qV kT x Ld p x Dx qD q p e e

dx L

J

NAp N

N N p0

N

( )( ) ( 1)

x LqV kTd n x D

x qD q n e edx L

J

n-side

p-side

p nN P N P0 0x x x x x x

J J J J J

A2 N Pi

N A P D

( 1)qV kTD D

qn eL N L N

J

pn Diode I–V Characteristic


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A

0

2 N P0 i

N A P D

( 1)qV kTI I e

D DI Aqn

L N L N

I A J

pn Diode I–V Characteristic


A2 N Pi

N A P D

( 1)qV kTD D

Aqn eL N L N

• Shockley Equation,for ideal diode

• I0 can be viewed as the drift current due to minority carriers generated within the diffusion lengths of the depletion region

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I0 can vary by orders of magnitude, depending on the semiconductor material, due to ni

2 factor.

In an asymmetrically doped pn junction, the term associated with the more heavily doped side is negligible.

If the p side is much more heavily doped,

If the n side is much more heavily doped,

2 NP0 i

P D N A

DDI Aqn

L N L N

2 P0 i

P D

DI Aqn

L N

2 N0 i

N A

DI Aqn

L N

Diode Saturation Current I0


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N P J J J

Diode Carrier Currents

N p n N p

P p n P n

( ) ( )

( ) ( )

x x x x

x x x x

J J

J J


• Total current density is constant inside the diode

• Negligible thermal R-G throughout depletion region dJN/dx = dJP/dx = 0

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n0p

p0p

p0n

n0n

Carrier Concentration: Forward Bias

A2

i qV kTnp n e

p A

n D

p N

n N

Excess minoritycarriers

Excess minoritycarriersA P

n n0( ) ( 1)qV kT x L

p x p e e NA

p p0( ) ( 1)x LqV kTn x n e e


Law of the Junction

Low level injection conditions

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Carrier Concentration: Reverse Bias


Deficit of minority carriers near the depletion region.

Depletion region acts like a “sink”, draining carriers from the adjacent quasineutral regions

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2

S CR A DBR bi

A D2

N NV V

q N N

E

A DCR bi BR

S A D

2 N NqV V

N N

E

• At breakdown, VA=–VBR

Breakdown Voltage, VBR


If the reverse bias voltage (–VA) is so large that the peak electric field exceeds a critical value ECR, then the junction will “break down” and large reverse current will flow.

Thus, the reverse bias at which breakdown occurs is

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2 A DCR BR

S A D

2 N NqV

N N

E

Small E-field:

High E-field:

Low energy, causing lattice vibration and localized heating only

High energy, enabling impact ionization which causing avalanche, at doping level N < 1018 cm–3

Breakdown Mechanism: Avalanching


• ECR : critical electric field in the depletion region

2

CRBR

2

sVqN

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Breakdown Mechanism: Zener Process


Zener process is the tunnelingmechanism in a reverse-biased diode.

Energy barrier is higher than the kinetic energy of the particle.

The particle energy remains constant during the tunneling process.

Barrier must be thin dominant breakdown mechanism when both junction sides are heavily doped.

Typically, Zener process dominates when VBR < 4.5V in Si at 300K and N > 1018 cm–3.

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Chapter 7pn Junction Diodes: Small-Signal Admittance


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V0 << VA

RS : serial resistanceC : capacitanceG : conductanceY : admittance

Small-Signal Diode Biasing

Chapter 7 pn Junction Diodes: Small-Signal Admittance

When reversed-biased, a pn junction diode becomes functionally equivalent to a capacitor, whose capacitance decreases as the reverse bias increases.

Biasing additional a.c. signal va can be viewed as a small oscillation of the depletion width about the steady state value.

Y G j C

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DCD

IC

kT q

sJC A

W

Junction / depletion capacitance,

due to variation of depletion charges

i

J DC C C av

1R G

Diffusion capacitance,

due to variation of stored minority charges in the quasineutral regions

Minority carrier lifetime

Total pn Junction Capacitance


• CJ dominates at low forward biases, reverse biases.• CD dominates at moderate to high forward biases.

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2

bi A2 2 2 2

J s B S

1 2( )

WV V

C A qN A

Relation Between CJ and VA

sbi A

B

2W V V

qN

NB : bulk semiconductor doping,

NA or ND as appropriate.


For asymmetrical step junction,

Therefore,

• A plot of 1/CJ2 versus VA is linear.

• The slope is inversely proportional to NB.• An extrapolated 1/CJ

2 = 0 intercept is equal to Vbi.

Semiconductor Device Physicseng.staff.alexu.edu.eg/~mmorsy/Courses/Undergraduate/EE336... ·...

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